Simple Interest
Math MCQs

Question :    If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $4984

Rate of Simple Interest (R) = 3%

Time (T) = 4 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$4984 = P (1 + 3% × 4)

⇒ $4984 = P (1 + ³/₁₀₀ × 4)

⇒ $4984 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4984 = P (1 + ¹²/₁₀₀)

⇒ $4984 = P (^{100 + 12}/₁₀₀)

⇒ $4984 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4984

⇒ P = ⁴⁹⁸⁴/_¹¹²/100

⇒ P = 4984 × ¹⁰⁰/₁₁₂

⇒ P = ^{4984 × 100}/₁₁₂

⇒ P = ⁴⁹⁸⁴⁰⁰/₁₁₂

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4984, then the Principal = ¹⁰⁰/₁₁₂ × 4984

= ^{100 × 4984}/₁₁₂

= ⁴⁹⁸⁴⁰⁰/₁₁₂

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.

(3) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(5) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

(6) How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?

(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.

(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?

(10) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.